Interlayer Valley Coupling and Hybridized Excitons in Twisted van der Waals Bilayers With Broken Translational Symmetry

ABSTRACT

Twisted van der Waals (vdW) bilayers allow the moiré potential and interlayer coupling to be tuned through the relative rotation between layers, providing a platform to study moiré physics. At large twist angles, the lack of translational symmetry allows intralayer and interlayer valley momenta to be connected by Umklapp processes, in principle permitting unconventional intervalley coupling. However, direct experimental evidence of such couplings in twisted vdW bilayers with broken translational symmetry has been limited. Here, we observe interlayer coupling between the K and −K valleys in twisted MoS₂ bilayers by detecting intense photoluminescence from high‐energy interlayer hybridized excitons. These hybridized excitons are absent in commensurate twisted MoS₂ homobilayers and display an almost vanishing valley Zeeman splitting, indicative of strong mixing between intralayer and interlayer excitonic states. This hybridization gives rise to an unusual magnetic‐field‐dependent valley polarization in excitons with distinct spin configurations. With increasing temperature, the hybridized excitons detune, and their energies approach those of intralayer excitons, revealing a sensitive interplay between moiré coupling and thermal effects. Our results uncover a key role of broken translational symmetry in excitons of twisted MoS₂ bilayers and open a route to exploring quantum phenomena in aperiodic twisted MoS₂ materials.

Breaking translational symmetry in large‐angle twisted MoS₂ bilayers enables Umklapp‐mediated interlayer coupling between the K and −K valleys, producing high‐energy hybridized excitons with strong photoluminescence, nearly vanishing valley Zeeman splitting, and temperature‐tunable detuning. These results identify aperiodic twist as a powerful handle for engineering unconventional moiré excitons and valley physics.

1. Introduction

Twisted vdW homobilayers and heterostructures offer a promising platform for exploring strongly correlated states [1, 2, 3] and exotic photonic effects [4, 5, 6, 7]. The key factor enabling these moiré phenomena is the long‐wavelength moiré patterns formed by the interlayer twist between adjacent atomic layers. These moiré superlattices modulate the interlayer electronic coupling and impose a periodic potential, leading to the formation of nearly flat electronic bands at small twist angles [2, 8, 9]. Flattened bands significantly suppress the kinetic energy of electrons, thereby amplifying the role of Coulomb interactions and giving rise to the emergence of correlated insulating states, superconductivity, and non‐trivial topological phases. In twisted graphene bilayers, flat bands are highly sensitive to the twist angle and appear only within a narrow range close to the so‐called “magic angle” (∼1.1°), where the interlayer hybridization and band displacement are optimally balanced [2, 10, 11]. This constraint limits the tunability and robustness of correlated phenomena in twisted graphene systems. Transition‐metal dichalcogenides (TMDs), by contrast, offer a distinct landscape. Their direct bandgaps, strong spin‐orbit coupling, and reduced dependence on external displacement fields allow the moiré potential to be tuned more continuously by twist angle [3, 12, 13]. As a result, moiré effects in TMD bilayers are observed across substantially broader angular ranges—typically from 0° to 5° for R‐type stacking and from 55° to 60° for H‐type stacking [3, 4, 5, 6, 9, 14, 15, 16, 17, 18, 19].

At larger twist angles, the moiré wavelength becomes shorter, and the associated flat‐band phenomena gradually diminish due to the reduced spatial periodicity and weaker interlayer modulation. Consequently, twisted bilayers with large twist angles remain largely unexplored, both experimentally and theoretically, despite potential opportunities for discovering novel electronic behaviors in these regimes. Interestingly, when the twist angle is incommensurate, the system lacks long‐range translational symmetry, preventing the formation of conventional electronic superlattices. In such quasi‐periodic structures, the lack of periodicity can give rise to many‐body effects that differ fundamentally from those in periodic moiré crystals [20, 21, 22, 23]. For example, recent investigations into 30° twisted graphene bilayers have unveiled the formation of multiple Dirac cones with 12‐fold rotational symmetry, a hallmark of Umklapp scattering processes unique to quasi‐crystalline systems [20, 24]. Strong interlayer coupling in these structures can substantially reconstruct the band structures, producing features such as mini‐gaps near the valence band maximum [25] and field‐tunable interlayer K–Q valley coupling [21], as recently reported in WSe₂ moiré quasicrystals. Theoretically, a variety of valley hybridization and scattering mechanisms are predicted to arise in twisted bilayers with broken translational symmetry [21, 25]. However, despite increasing interest in these quasi‐periodic moiré systems, experimental realizations remain sparse, leaving many predicted phenomena unverified and motivating further investigations.

Here, we report the discovery of high‐energy hybridized interlayer excitons in twisted MoS₂ bilayers with broken translational symmetry, observed at twist angles of 11° and 30°. These hybridized excitons arise from coupling between a hole in the K valley and an electron in the −K valley, which further hybridizes with intralayer excitons through K‐(−K) interlayer coupling. Notably, these excitons exhibit an almost negligible Zeeman valley effect under magnetic fields, with a g‐factor of approximately ‐0.6, which depends on the coupling strength between intralayer and interlayer excitons. Moreover, temperature‐induced detuning shifts the energy of the interlayer excitons closer to that of intralayer excitons at elevated temperatures. These findings demonstrate the potential of aperiodic moiré crystals to explore novel moiré photonics and quantum phenomena.

2. Results and Discussion

2.1. Interlayer Valley Coupling and Interlayer Hybridized Excitons

Figure 1a illustrates the dodecagonal quasicrystal structure of a twisted MoS_2​ homobilayer with a 30° twist angle (30°‐THS). This configuration, characterized by broken translational symmetry, lacks a moiré mini‐Brillouin zone in momentum space. As a result, Umklapp scattering facilitates the approach of intralayer and interlayer valley momenta [20, 25], allowing a range of unconventional valley couplings. In the 30°‐THS, there is a significant valley mismatch between the K valley of the top layer (K _t ) and the K or −K valleys of the bottom layer (K _b ​ or −K _b ). Through the Umklapp scattering, the K or –K valley in the upper (lower) layer is scattered to lower (upper) with the scattering condition K_t + G_t = K_U + G_b, as depicted in the first‐order Umklapp process in Figure 1b. The valleys become closer through high‐order Umklapp scattering (Figure S1), which mitigates the valley momentum mismatch. This enables interlayer valley coupling of K _t​ ‐K _b ​ or K _t​ ‐(−K _b ). The K‐K valley coupling between layers has been reported in the H‐type MoS₂ bilayer, whereas it is suppressed in R‐type stacked MoS₂​ bilayers due to symmetry constraints [26, 27], which results in interlayer charge transfer and the formation of interlayer excitons. Interlayer K‐(‐K) coupling is generally unlikely in a natural bilayer. However, in the moiré quasicrystal, such coupling can be allowed and can give rise to a new‐type hybridized interlayer exciton (Figure 1c), where the interlayer exciton (IX) couples with the A exciton (X_A). This hybridized IX (HIX^M), arising from moiré quasicrystal, differs from the hybridized IX coupled with the B exciton (X_B), which has been widely reported in 2H‐MoS₂ bilayers [28, 29, 30, 31], implying the different exciton behaviors between them (Note S3).

FIGURE 1.

Hybridized interlayer excitons in a moiré quasicrystal. (a) Moiré quasicrystal structure of the 30° twisted MoS₂ bilayer (30°‐THS). (b) Umklapp scattering in the Brillouin zones (BZ) of the 30° MoS₂ moiré quasicrystal. Blue and orange denote the BZs of the top and bottom layers, respectively. The K valley of the top layer (K_t) and the –K valley of the bottom layer (–K_b) are brought into momentum alignment via Umklapp scattering, enabling interlayer K–(–K) valley coupling. G_b and G_t represent the reciprocal lattice vectors of the bottom and top layers, respectively, with superscript 1 indicating first‐order Umklapp scattering. K _U (–K _U ) corresponds to the Umklapp scattering of the K (–K) valley. (c) Valley energy level diagram for the K and –K valleys in adjacent layers (L1 and L2). The moiré quasicrystal‐induced K–(–K) coupling hybridizes interlayer A (B) excitons with intralayer A (B) excitons, forming hybridized interlayer excitons (HIX_A ^M​ and HIX_B ^M). (d,e) Atomic‐resolution high‐angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image of 30°‐THS (d) and its amplified image (e). (f) Experimentally measured PL (left axis) and reflectance contrast (right axis) spectra of the 30°‐THS compared with monolayer MoS₂ (1L MoS₂), 0° MoS₂ homostructure (0°‐THS), and 60° MoS₂ homostructure (60°‐THS). In the 30°‐THS, two distinct high‐energy peaks—${HIX}_A^M$ (between A and B excitons) and ${HIX}_B^M$ (above B exciton)—are observed in both PL and reflectance contrast spectra but are absent in the other samples. g, Time‐resolved photoluminescence of 30°‐THS for ${HIX}_A^M$ peak. The hollow points represent the measured data, while the solid curve denotes the fitting result using the decay index equation I(t) ∝ exp (‐t/τ). The fitting parameter τ is ∼1.0 ns, revealing the exciton lifetime of ∼1.0 ns.

To explore interlayer valley coupling in twisted vdW bilayers, we fabricated 30°‐THS samples via chemical vapor deposition (CVD) growth (Figure S2) and characterized their photoluminescence (PL) and reflectance contrast spectra. The detailed fabrication process is provided in the Methods section. The atomic‐resolution high‐angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image of 30°‐THS (Figure 1d,e) clearly shows the dodecagonal rotational symmetry. Figure 1f compares the PL and reflectance contrast spectra of 30°‐THS with those of 0° and 60° aligned MoS₂​ bilayers (0°‐THS and 60°‐THS). The conventional excitons including trion (X_T​), X_A​, and X_B​ emissions are observed and exhibit similar exciton energy in all PL spectra (Figure 1f). However, two prominent new resonant peaks (${HIX}_A^M$ and ${HIX}_B^M$) appear at 1.938 and 2.090 eV in the PL and reflectance contrast spectra of 30°‐THS, respectively. These peaks, located ∼68 and ∼88 meV above X_A​ and X_B, respectively, are attributed to reduced exciton binding energy [32] due to spatial separation of electrons and holes across different layers. These peaks are distributed throughout the 30°‐MoS₂ moiré quasicrystal and exhibit nearly consistent energy position, as confirmed by the spatial PL mapping (Figure S3). The hybridized excitons exhibit narrower FWHM and comparable PL intensities relative to the corresponding intralayer excitons. The strong resonant intensity of hybridized excitons is attributed to the strong interlayer valley coupling, promoting the interlayer radiative recombination in the moiré quasicrystal. To verify the interlayer nature of the newly observed PL peaks, we performed time‐resolved photoluminescence (TRPL) measurements. The exciton lifetime of ∼1.0 ns for ${HIX}_A^M$ (Figure 1g) is obtained by fitting TRPL using a decay index equation I(t) ∝ exp (‐t/τ). The exciton lifetime of ${HIX}_A^M$ is 2–3 orders of magnitude longer than the typical lifetimes of intralayer excitons in TMDs [33, 34, 35], which implies that the new high‐energy peaks possess the features of interlayer excitons. Moreover, the PL intensity of these hybridized excitons exhibits an approximately linear dependence on excitation power (Figure S11), similar to intralayer excitons but distinct from purely interlayer excitons in type‐II heterostructures. This near‐linear power dependence suggests that recombination of the hybridized excitons is not dominated by second‐order power‐dependent nonradioactive channels [36]. In addition, the emission peak exhibits a weak power‐dependent blueshift (Figure S11), indicating finite dipolar repulsive interactions. The small magnitude of this shift is consistent with a hybrid exciton with partial interlayer character and a moderate effective dipole moment.

2.2. Valley Zeeman Splitting of Interlayer Hybridized Excitons in Moiré Quasicrystal

These hybridized‐state excitons can be universally measured through PL spectroscopy measurements in our manufactured 30°‐THS, as confirmed by PL mapping (see Figure S2), providing a convenient platform to study interlayer hybridized excitons. To explore the characteristics of these excitons, we investigate their valley Zeeman effect under an external magnetic field in Faraday geometry. When a magnetic field is applied to the moiré quasicrystal, Zeeman shifts occur in the K and –K valleys (Figure 2a,b), governed by the total magnetic moment. There are three primary contributions: spin (µ _spin ), orbital (µ _orbital ), and valley (µ _valley ) magnetic moment [30, 37, 38]. The spin contributions from the valence and conduction bands counterbalance each other due to the same spin states of electrons and holes in spin‐conserved exciton emissions. For the intralayer exciton, the effective magnetic moment primarily originates from the orbital contribution, while for the interlayer exciton, it stems from both orbital and valley contributions [37]. These contributions lead to distinct Zeeman shifts, ΔE_intra = −2Δ _orb and ΔE_inter = 2Δ _orb + 2Δ _valley (Δ _orb and Δ _valley are the shifts for orbital and valley contribution) in MoS₂ vdW materials, respectively. Therefore, the theoretical g‐factors for intralayer and interlayer A excitons are g _A = −3.6 and g _IX = 12, respectively. However, hybridization between interlayer and intralayer excitons modifies the effective g‐factor of HIX^Ms, depending on the degree of hybridization. Experimental studies have revealed the g factors of ∼4.2 [30] and ∼−1.9 [39] for hybridized excitons in MoS₂ and MoSe₂ bilayers, which can be further tuned by detuning hybridized exciton states with an external electric field.

FIGURE 2.

Valley splitting and valley polarization of hybridized excitons under a magnetic field. (a,b) Schematic valley energy level diagrams for σ⁺ (a) and σ⁻ (b) excitation. Dotted curves represent valley in the absence of a magnetic field, while solid curves denote the case at B<0. Pink and blue arrows represent spin up and spin down, respectively. (c) Calculated g‐factors of ${HIX}_A^M$ and ${HIX}_B^M$ as a function of coupling strength (η). Squares and circles represent calculated g‐factor detuning for interlayer exciton using Equation (1), while the red stars correspond to the measured values. (d,e) Color plots of PL spectra under varying magnetic field for σ⁺ (d) and σ⁻ (e) emissions, showing minimal PL peak shifts. Black dotted lines indicate trends in PL peak positions under the magnetic field. (f) Zeeman splitting of ${HIX}_A^M$ (pink) and ${HIX}_B^M$ (blue), exhibiting g‐factors of −0.6 and −3.5, respectively. Solid lines represent fitting results using ΔE = gµ _B B with Bohr magneton µ _B = 0.0578 meV/T. (g) Valley polarization spectra (lower panel) and degree of circular polarization (DOCP; upper panel) for the 30°‐THS under σ⁺ excitation. (h) DOCP of ${HIX}_A^M$ and ${HIX}_B^M$ under σ⁺ (orange balls) and σ⁻ (blue balls) excitation in a magnetic field, displaying “X” and “V” shape, respectively. Solid lines denote the linear fits.

We used a phenomenological model [30] to obtain the relationship between effective g factor of HIX^Ms and their coupling strength:

$$g_{\pm }^{eff}={\partial }_{B_z}{(\hslash \omega )}_{\pm }{|}_{B_z=0}=\frac{(g_A+g_{IX})}{2}\mp \frac{(g_A-g_{IX})\mathrm{\Omega }}{4\sqrt{{\eta }^2+\frac{{\mathrm{\Omega }}^2}{4}}}$$ (1)

where η and Ω denote the coupling strength and detuning energy, respectively. −(+) corresponds to interlayer (intralayer) transitions. The detailed discussion is provided in Note S1. This equation suggests that the effective g‐factor ($g^{eff}$) of ${HIX}_A^M$ is correlated with the coupling strength η and detuning parameter Ω. The Ω can be controlled by the electric field, leading to a variation in the $g^{eff}$, assuming the electric field has a minor effect on η. For 2H‐MoS₂ and 2H‐MoSe₂ bilayers, the g‐factors were tuned from 4.2 to 7 [30] and from −1.9 to 11.8 [39] under an electric field, respectively. In detuning interlayer transition, using the experimentally measured g _intra (g_A = −11.5 and g_B = −8.4; see Figure S4), theoretically estimated g _inter = 12, and Ω = ‐0.04 eV, the dependence of g‐factors for HIX^Ms on coupling strength η was plotted (Figure 2c and Figure S5).

The consequence of hybridization between intralayer and interlayer excitons is a reduction in the valley Zeeman splitting, compared to that of the corresponding intralayer or interlayer excitons. Figure 2d,e presents color plots of circularly polarized PL spectra, showing minimal peak shifts for ${HIX}_A^M$ as the magnetic field varies for right (σ⁺) and left (σ⁻) circularly polarized emissions. This behavior contrasts with the interlayer hybridized excitons typically observed in MoS₂​ and MoSe_2​ bilayers [30, 39, 40], as well as in the moiré quasicrystals of WSe₂​ [21]. The Zeeman splitting is around 0.4 and 2.3 meV under 9 T magnetic field, corresponding to estimated g factors of −0.6 and −3.5 for the ${HIX}_A^M$ and ${HIX}_B^M$ (Figure 2f), respectively, using ΔE = gµ _B B (µ _B and B are the Bohr magneton and magnetic field, respectively). Such small valley splitting is attributed to the strong hybridization between intralayer and interlayer excitons induced by moiré quasicrystal. The coupling strength is approximately 0.274 and 0.032 meV (red stars in Figure 2c), indicating the stronger hybridized state in ${HIX}_A^M$ due to closer in energy in comparison to ${HIX}_B^M$. These results underscore the unique Zeeman effect in moiré quasicrystal, distinguishing them from natural bilayers and heterostructures.

Moreover, ${HIX}_A^M$ (${HIX}_B^M$) exhibits the same sign of valley polarization and a larger degree of circular polarization (DOCP) than intralayer A (B) exciton (Figure 2g). Here, the DOCP =$(I_{{\sigma }^{+/-}}-I_{{\sigma }^{-/+}})/(I_{{\sigma }^{+/-}}+I_{{\sigma }^{-/+}})$ is identified, where $I_{{\sigma }^{+/-}}$ represents the PL intensity for σ⁺ (σ⁻) emissions under σ⁺ (σ⁻) excitation. Intravalley component ensures the sign of valley polarization, while the interlayer component enhances valley polarization due to reducing intervalley scattering. When a magnetic field is applied, the ${HIX}_A^M$ follows the magnetic‐field‐dependent valley polarization trend of X_A, showing a significant “X” shape, in contrast to the moderately “V” shape in ${HIX}_{\mathrm{B}}^M$ (Figure 2h). These differences suggest distinct valley process under magnetic field for ${HIX}_A^M$ and ${HIX}_B^M$. Hybridized interlayer excitons require electron interlayer tunneling for their formation, thus their valley‐conserving and valley‐flipping rates can be described by corresponding rates of intralayer neutral exciton and interlayer hybridized degree, i.e. ${\gamma }_1^{HI{X}_A^M}={\alpha }_A{\gamma }_1^A{\chi }_1^A$ (${\gamma }_1^{HI{X}_B^M}={\alpha }_B{\gamma }_1^B{\chi }_1^B$) and ${\gamma }_2^{HI{X}_A^M}={\beta }_A{\gamma }_2^A{\chi }_2^A$ (${\gamma }_2^{HI{X}_B^M}={\beta }_B{\gamma }_2^B{\chi }_2^B$), where ${\gamma }_1^i$ and ${\gamma }_2^i$ represent valley‐conserving and valley‐flipping rate for corresponding exciton, respectively. α, β, and χ are the valley‐conserving, valley‐flipping coefficient, and the interlayer conversion rate, respectively. For ${HIX}_A^M$, $\frac{{\chi }_1^A}{{\chi }_2^A}$ follows the changes of $\frac{{\gamma }_1^A}{{\gamma }_2^A}$ at a magnetic field due to the Zeeman effect tuning K valley approaching –K valley for different layers under σ⁺ excitation which reduces their energy difference (Figure S6). Consequently, it has $\frac{{\gamma }_1^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}<0,{\sigma }^{-}\right)}{{\gamma }_2^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}<0,{\sigma }^{-}\right)}>\frac{{\gamma }_1^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}=0,{\sigma }^{-}\right)}{{\gamma }_2^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}=0,{\sigma }^{-}\right)}>\frac{{\gamma }_1^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}>0,{\sigma }^{-}\right)}{{\gamma }_2^{{\mathrm{HIX}}_{\mathrm{A}}^{\mathrm{M}}}\left(\mathrm{B}>0,{\sigma }^{-}\right)}$, that is “X” shape. Conversely, $\frac{{\chi }_1^B}{{\chi }_2^B}$ has the opposite changes to the $\frac{{\gamma }_1^{\mathrm{B}}}{{\gamma }_2^B}$ owing to the opposite spin in B exciton compared to A exciton, resulting in a moderate magnetic field effect for ${HIX}_B^M$. The detailed discussion is provided in Note S2.

2.3. Hybridized Excitons in Twisted MoS₂ Bilayers With Broken Translational Symmetry

Hybridized interlayer exciton can exist in the twisted MoS₂ homobilayers with broken translational symmetry, without the need for a moiré quasicrystal, as these systems also create the conditions necessary to couple K and –K valleys across different layers via Umklapp process. In twisted TMD bilayers, moiré crystals form only at specific commensurate twist angles, determined by the condition [41]:

$$\cos ({\theta }_i)=\frac{\left(3i^2+3i+0.5\right)}{\left(3i^2+3i+1\right)}$$ (2)

where i is an integer. Commensurate angles for i up to 20 are listed in Table S1. At incommensurate angles, translational symmetry is disrupted, providing a unique platform for exploring exotic moiré phenomena.

To confirm this, we further fabricate twisted MoS₂ homobilayers with twist angles of 11° ± 0.3°, 13.2° ± 0.3°, 21.8° ± 0.3°, and an additional 30°‐THS sample synthesized by CVD. The polarization SHG measurements of these samples were performed to determine the twist angle (Figure S7), and their Raman spectra show twisted‐angle‐dependent vibration properties (see Figures S14, S15 and Note S5). Their corresponding PL and reflectance contrast spectra are shown in Figure 3a, with peak positions for MoS₂ homobilayers at each twist angle presented in Figure 3b. Two high‐energy peaks corresponding to ${HIX}_A^M$ and ${HIX}_B^M$ are prominently observed in the 11°‐THS and 30°‐THS samples, highlighting the crucial role of broken translational symmetry for interlayer exciton in moiré superlattice. Notably, although the calculated band structures exhibit an indirect bandgap (Figure S8), the dominant intralayer PL emission in twisted MoS₂ bilayers still originates from strong K–K excitons, supporting the K/–K valley coupling for hybridized interlayer excitons. The PL mapping of ${HIX}_A^M$ clearly shows the uniform spatial distribution in 11°‐THS, but not in 13.2°‐THS and 21.8°‐THS (Figure 3c; Figures S12 and S13). Compared with the 11°‐THS, the hybridized interlayer excitons in the 30°‐THS appear at lower energy, reflecting the lower‐energy intralayer excitons in the 30° structure due to twisted‐angle‐dependent band structure and moiré potential. Moreover, the energy separation between the intralayer and hybridized excitonic peaks is larger in 30°‐THS (Figure 3b), consistent with stronger hybridization. These results indicate that both the twist‐angle‐dependent feature of intralayer excitons and the strength of interlayer coupling affect the hybridized interlayer excitons. In contrast to the commensurate moiré crystals at the twist angle of 13.2° and 21.8°, the PL mapping of incommensurate stacked 11°‐THS sample shows bright and uniform ${HIX}_A^M$ signal with a central energy of 1.931 eV and an integral width of 29 meV. Additionally, we examined the valley Zeeman effect and valley polarization in the 11° sample under an external magnetic field. The ${HIX}_A^M$ exhibits negligible Zeeman splitting (Figure 3d), with a g‐factor of approximately −0.8, comparable to the 30° sample. The magnetic field effects on valley Zeeman splitting (Figure 3d) and valley polarization (Figure 3e) show consistent behavior across the 11° and 30° samples, highlighting the robustness of interlayer hybridized excitons under these conditions. These results confirm that broken translational symmetry in twisted MoS₂​ bilayers plays a pivotal role in the emergence and optical properties of interlayer hybridized excitons, offering a compelling avenue for studying moiré physics in systems beyond commensurate angles.

FIGURE 3.

Hybridized interlayer exciton in twisted vdW bilayers without translational symmetry. (a) PL and reflectance contrast spectra of twisted MoS₂ homobilayers at selected twiste angles, showing a prominent ${HIX}_A^M$ and ${HIX}_B^M$ peaks for 11°‐THS and 30°‐THS. (b) PL peak positions as a function of twist angle. (c) Samples (upper panel) and PL mapping (lower panel) for 11°‐THS (left panel), 13.2°‐THS (middle panel), and 21.8°‐THS (right panel). The PL mappings, centered at 1.931 eV with a 29 meV width, reveal a significant bright area at 11°‐THS. Scale bars in optical images are 10 µm. (d) Zeeman splitting as a function of magnetic field for ${HIX}_A^M$ (red balls) and ${HIX}_B^M$ (blue balls) in 11°‐THS, showing g factor of −0.8 and −3.6, respectively. (e) DOCP of ${HIX}_A^M$ and ${HIX}_B^M$ as a function of magnetic field in 11°‐THS under σ⁺ (orange balls) and σ⁻ (blue balls) excitation, which exhibits a pronounced “X” shape for ${HIX}_A^M$ and a minor “V” shape for ${HIX}_B^M$.

2.4. Temperature‐Dependent Detuning of Hybridized Exciton Energy

The hybridized interlayer excitons in the 2H‐MoS₂ bilayer exhibit remarkable thermal stability [28], persisting even at room temperature. To investigate the temperature dependence of hybridized interlayer excitons in moiré quasicrystal, we measured temperature‐dependent PL and reflectance contrast spectra of 30°‐THS. The room‐temperature ${HIX}_A^M$ and ${HIX}_B^M$ were clearly observed in both the PL (Figure 4a) and reflectance contrast (Figure 4b) spectra, with both excitons undergoing a redshift as the temperature increased from 1.65 to 300 K. We used the O'Donnell and Chen model [42] to fit the temperature‐dependent peak positions, with the fitting results showing in good agreement with our experimental data (Figure 4c; Table S2). Compared to intralayer exciton (Figures S9 and S10), ${HIX}_A^M$ and ${HIX}_B^M$ undergo faster energy shifts with increasing temperature, gradually approaching X_A and X_B, respectively. The energy differences between ${HIX}_A^M$ (${HIX}_B^M$) and X_A (X_B) gradually decline from ∼70 (∼85) at low temperature to ∼50 (∼55) meV at room temperature (Figure S9), potentially indicating the HIX^Ms detuning interlayer exciton.

FIGURE 4.

Temperature‐dependent PL and reflectance contrast spectra in moiré quasicrystal. (a) Color plots of temperature‐evolution PL spectra for 30°‐THS. (b) Reflectance contrast spectra of 30°‐THS at selected temperatures, showing a blueshift as the temperature decreases by 1.65 K. Dotted lines are used to show the trends of ${HIX}_A^M$ and ${HIX}_B^M$ with temperature. (c) PL peak positions as a function of temperature, displaying a faster redshift for hybridized excitons than that for intralayer excitons. Solid lines represent the fitting results based on temperature‐dependent bandgap equations (see Note S4). The blue and cyan balls represent the calculated energies of ${HIX}_A^M$ and ${HIX}_B^M$, respectively, by Equation (3) with temperature‐dependent detuning energy (see main text). The reduced energy gap between hybridized excitons and intralayer excitons signifies the hybridized interlayer excitons detuned to intralayer excitons. (d) Valley polarization spectra at selected temperature (1.65, 150, and 300 K). (e) Valley polarization as a function of the temperature, revealing a decreasing trend with increasing the temperature. The valley polarization of hybridized excitons declines faster than the corresponding intralayer excitons as the temperature increases.

We rewrite HIX^Ms energy in the absence of a magnetic field, which can be expressed as:

$$E_{HI{X}^M}(T)=E_{intra}(T)+\frac{\mathrm{\Omega }(T)}{2}+\sqrt{\frac{\mathrm{\Omega }{(T)}^2}{4}+\eta {(T)}^2}+c$$ (3)

Here, the coupling strength η and detuning parameter Ω are the functions of temperature, and c is the correction constant. Assuming that the coupling strength η remains constant with temperature, the Ω(T) alone detunes the energy of HIX^Ms. We use the values of η = 0.274 (0.032) meV obtained from g factor (Note S1) and c = 0.1811 (0.0792) eV for ${HIX}_A^M$ (${HIX}_B^M$), thus the Ω(T) can be estimated based on our experimental data. The resulting energy of HIX^Ms calculated by Equation (3) with temperature‐dependent Ω(T) is shown in blue and cyan balls of Figure 4c. The decreasing Ω(T) (Table S3) suggests detuning the interlayer exciton as the temperature increases. Furthermore, owing to temperature‐induced detuning, the valley polarization of the hybridized interlayer excitons gradually approaches that of the corresponding intralayer excitons as the temperature increases (Figure 4d). At low temperature (1.65–100 K), the valley polarization exhibits only a weak temperature dependence, indicating limited intervalley scattering. However, beyond 100 K, the valley polarization gradually decreases due to the phonon‐induced intervalley scattering (Figure 4e), which is consistent with the previous results on TMDs [43, 44, 45, 46]. Compared with the intralayer excitons, the hybridized excitons show a faster decline, consistent with the reduced hybridization at elevated temperature, which weakens the hybridization‐induced valley‐polarization enhancement. As a result, at high temperature the valley polarization of the hybridized excitons becomes comparable to that of the intralayer excitons. A previous version of this work has been deposited on a preprint server [47].

3. Conclusion

In summary, we have experimentally demonstrated a distinctive form of interlayer momentum coupling in twisted MoS₂ bilayers with broken translational symmetry, leading to the emergence of exotic hybridized interlayer excitons. In particular, we resolve interlayer K–(−K) valley coupling that gives rise to high‐energy excitons with an almost vanishing valley Zeeman splitting and an effective g‐factor of about −0.6 in the MoS₂ moiré quasicrystal. This strongly suppressed Zeeman response originates from strong hybridization between intralayer and interlayer excitons, which compensates the opposite Zeeman shifts of their constituent states. The resulting strong resonant photoluminescence offers a sensitive optical handle for probing the features of hybridized excitons and for designing tunable valleytronic devices. Our findings reveal the uniqueness and complexity of twisted MoS₂ bilayers with broken translational symmetry and establish a connection between symmetry breaking and hybridized excitonic states in twisted MoS₂ systems. Furthermore, motivated by the previously observed interlayer K‐Q coupling in WSe₂/WSe₂ moiré quasicrystals [21] and our experimental observation of interlayer K‐(‐K) coupling in incommensurate twisted MoS₂ bilayers, we expect that a broader family of unconventional valley couplings should be accessible in translational‐symmetry‐broken twisted systems.

4. Methods

4.1. Sample Preparation

Twisted MoS₂​ homobilayers were synthesized using a space‐confined chemical vapor deposition (CVD) method. A small quartz tube (12 mm in diameter) containing two back‐to‐back SiO₂​/Si substrates (40 mm in length and 9 mm in width) was placed inside a 1‐inch quartz tube within a high‐temperature furnace (OTF‐1200X). A precursor mixture of MoO₃​ (0.8 mg) and NaCl, in a 1:20 molar ratio (MoO₃​: NaCl), was positioned 10 mm from the substrates and the front opening of the quartz tube. Sulfur powder (0.1 g) was placed in a crucible, located 12 cm away from the precursors. During the growth process, the reaction was conducted under a high‐purity Ar atmosphere maintained at a flow rate of 50 sccm and ambient pressure. The temperature was ramped to 780°C at a rate of 30°C/min, held for 5 min, and then allowed to cool naturally to room temperature. This process yielded twisted MoS₂​ homobilayers on the SiO₂​/Si substrates. Details of the synthesis process are available in Ref [48]_.

4.2. Optical Measurements

PL and Raman spectroscopy measurements were performed using a WITec CryoRaman system equipped with a continuous‐wave (CW) 532 nm laser and a ×70 objective lens, providing a light spot diameter of approximately 1 µm. Optical gratings with 1800 and 150 g mm⁻¹ were used for Raman and PL measurements, respectively. Samples were loaded into a closed‐cycle cryostat (attoDRY2100 system) equipped with a superconducting magnet capable of generating a magnetic field of up to 9 T in the Faraday geometry. The cryostat allowed measurements at temperatures as low as 1.65 K. Circularly polarized PL spectra were obtained by detecting right circular polarization (σ⁻) and left circular polarization (σ⁺) emissions under σ⁺ and σ⁻ excitations, respectively. A white LED light source was used for reflection spectroscopy. Reflectance contrast spectra were calculated using the formula

$$\frac{R-R_0}{R+R_0}$$

where R is the reflected light intensity from the sample, and R₀​ is the reflected light intensity from the substrate.

4.3. Density Functional Theory (DFT) Calculations

Electronic structure calculations for twisted MoS_2​ bilayers with twist angles of 13.2° and 21.8° were performed using the Vienna Ab initio Simulation Package (VASP) [49] based on density functional theory (DFT). The exchange‐correlation functional was modeled using the Perdew–Burke–Ernzerhof (PBE) [50] form. Ionic positions and lattice parameters were relaxed until electronic energy and ionic forces converged to less than 10⁻⁶ eV and 10⁻⁴ eV/Å, respectively. For the 13.2° twisted homobilayer structure (THS), a 3 × 3 × 1 k‐point mesh was used, while a 5 × 5 × 1 k‐point mesh was adopted for the 21.8° THS. A plane‐wave energy cutoff of 500 eV was applied and van der Waals interactions were included using the Grimme DFT‐D3 method [51].

Author Contributions

Y. P. L. conceptualized the project. X. X. performed cryogenic optical characterizations, including Raman and photoluminescence measurements. Sample loading into the cryostat was carried out by X. X., J. Y. C., S. F. L., and J. N. D. X. W. W synthesized the samples. Data analysis and interpretation were led by X. X., Z. W. L., and Y. P. L. J. T. W. and X. X. conducted theoretical calculations using density functional theory (DFT) and provided related insights. The manuscript was drafted collaboratively by Y. P. L., X. X., and Z. W. L., with extensive revisions and contributions from all authors.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: adma73772‐sup‐0001‐SuppMat.pdf.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author on reasonable request.